Many wireless sensor networks require sufficient sensing coverage over long periods of time. To conserve energy, a coverage maintenance protocol achieves desired coverage by activating only a subset of nodes, while allowing the others to sleep. Existing coverage maintenance protocols are often designed based on simplistic sensing models that do not capture the stochastic nature of distributed sensing. We propose a new sensing coverage model based on the distributed detection theory, which captures two important characteristics of sensor networks, i.e., probabilistic detection by individual sensors and data fusion among sensors. We then present three coverage maintenance protocols that can meet the specified event detection probability and false alarm rate. The centralized protocol only activates a small number of sensors, but introduces extremely long coverage configuration delay. The Se-Grid protocol reduces the configuration time by dividing the network into separate fusion groups, but increases the number of active sensors due to the lack of collaboration among sensors in different groups. In contrast, by coordinating overlapping fusion groups, the Co-Grid protocol can effectively reduce the number of active sensors and the coverage configuration time. The advantages of Co-Grid have been validated through simulations and benchmark results on Mica2 motes.